Assessment 218: a learned fixed envelope for growing support

12 October 2026. Research assessment; scheduled completion 123. Written native construction 73, no root-ledger admission or external novelty claim.

Result

The complete argument supplies a charged producer and literal negative query reader for a stronger version of the combined-budget target. The first two distinct actual targets determine a shared prefix and a fixed suffix cube. Later targets fill existing coordinates; no old row or budget changes merely because global support grows. Actual aliases pay pending union through a checked final ambient mixed budget. The number of subsequent target births and both alias/target length ratios are unrestricted.

This does not close the moving observed-support budget problem. A singleton in the two-point support consisting of opposite cube corners has support mixed count one but ambient count equal to suffix width. Absent cylinders are charged. Constructions 71 and 72 remain separate positive classes, and assessment 217’s common-directory obstruction remains valid.

Independent adversarial review and repairs

The independent reviewer inspected construction 71, the maintained producer sections 32.3 and 32.7, the proposed bootstrap, then the complete final proof. The initial proposal risked stale dictionary writeback when the second alias differed from the first. The repaired implementation keeps the first alias in one distinguished explicit row outside the dictionary forever. Ordinary alias bits pay both comparison and dictionary lookup; no unresolved pointer or old path overwrites a newer dictionary root.

The review checked strict forward storage of the first target, streamed discovery of the prefix and suffix rulers, both initial-alias cases including suffix width one, exact signed budget changes, final sign gate, constant local child views, paid call and return work, complement-pair selection followed by another alias, prefix/width validation on negative queries, immutable old-top semantics and the inherited fixed-batch physical-node transfer. The final draft was approved against the established native primitive contracts. “First-name FIFO” was clarified to “first-target FIFO.”

The theorem extends the existing cube-budget method through a charged learned envelope; it is not a new general union algorithm. The common target width, common alias width, distinct first two targets, ambient budget and serial reuse remain explicit gates. Native recognition supplies a PEG for reversal of the complete checked language.

Independent finite evidence

The readable audit source checks literal-set semantics and recursive splice calls independently of the written bounded-batch schedule. It passed 620 bootstrap cases, 15,810 bootstrap literal queries, 6,360 signed-budget updates, 16,656 retained membership comparisons, 400 growing-support records, 19,840 growth snapshot queries, 45 pending-selection jobs, 774 immediate queries, 15 exact complement-pair costs and 23 ambient-gap examples. Same and different initial aliases, depth one, long prefixes, off-prefix pins, wrong widths, budget recovery and old snapshots are included.

These are finite mathematical experiments. Python sets, recursion and integer counters are not a native implementation or a timing benchmark. The native claim is the written schedule using previously established immutable primitives.

Validation and publication

Full repository verification and scoped reading, build, route, equation, link and source-download checks are recorded in the integration receipt after completion. Publication uses the pinned GitLab site projection. This research assessment is not the dedicated editorial or primary-proof review slot. No primary paper has been newly counted and no root claim is promoted. Browser viewport inspection is not claimed.

Next decisive test and accounting

Eliminate the absent-cylinder charge while allowing support growth after many completed rows. First study sparse suffix supports inside the learned envelope and one late branch insertion. Maintain the observed-support combined budget and aligned views with a paid repair schedule, or supply a different exact union/readout operation with its own charged deadline. Removing the two-distinct-initial-record gate, variable alias service widths and independently prepared store joins are separate extensions.

Scheduled 122 to 123 and mathematical 135 to 136, each once. Mathematical window two; last six-result reassessment 134 and last primary/editorial assessment 215 retained. Native construction 72 to 73. Next scheduled completion 124 is research, dedicated primary review 125, editorial 126. Legacy reverse-writer retirement remains a separate unverified follow-up.